Question 19151: OK...Brent rides a moped at 24 miles per hour. His wife Jan rides in the opposite direction at 8 miles per hour. How much time will pass when they are 24 miles apart? I know the answer is 3/4 hour, but I'm having a hard time getting that using the old rate x time = distance method. Can you bail me out?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Brent rides a moped at 24 miles per hour. His wife Jan rides in the opposite direction at 8 miles per hour. How much time will pass when they are 24 miles apart? I know the answer is 3/4 hour, but I'm having a hard time getting that using the old rate x time = distance method. Can you bail me out?
I'm having a hard time getting that using the................................ old rate x time = distance method. Can you bail me out?
your formula is ok but you have to understand relative speed cocept and use it ..it is as follows
Brent rides a moped at 24 miles per hour...so in one hour he goes 24 miles in one direction
His wife Jan rides in the opposite direction at 8 miles per hour...so in one hour she goes 8 miles in opposite direction.
so initially if they were together ,after 1 hour their distance of seperation is 24+8=32 miles as they were going in opposite directions.(just for your idea if they were going in same direction their distance of seperation would have been 24-8=16 miles)
so now we define relative speed as sum of the 2 speeds if they are in opposite directions (and difference between 2 speeds ifthey are in same direction)
so relative speed in this case =24+8=32 mph
now for distance again you have to consider 2 aspects ..one...what is the distance between them at start it is 0 here as they started at the same place.....next...we have to use the distance between them at the end ..here it is 24 miles ...so the additional distance of seperation between them from begining to end is 24-0=24(had the start been not 0 distance ,you will account for that here)
now for time same way as above for distance..both started at same time ...so begining time =0
end time = not known =t say...so difference in time =t-0=t
now you can use your formula with 3 new terms..relative speed ,difference in distance,difference in time,inplace of speed ,distance and time....so we get
rate x time = distance....gives
32*t=24
t=24/32=3/4 hour =3*60/4 =45 mts....hope it is clear...
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